arXiv subjects

Pawel Kurzynski

Publications and source records attributed to Pawel Kurzynski.

At least 37 records · Page 2Linked to original sources

arXiv2019

A little bit of classical magic to achieve quantum speedup

We introduce nebit, a classical bit with a signed probability distribution. We quantify its entropy using Szekely theorem on signed probability measures and show that classical stochastic dynamics supplemented with nebits can achieve or even exceed the speedup of Grover's quantum search algorithm. The proposed classical dynamics never reveals negativity of nebits and thus we do not need any operational interpretation of negative probabilities. We argue that nebits can be useful as a measure of non-classicality as well as a tool to find new quantum algorithms.

quant-ph↗

arXiv2019

Attractors and asymptotic dynamics of open discrete-time quantum walks on cycles

Open quantum walks often lead to a classical asymptotic behavior. Here, we look for a simple open quantum walk whose asymptotic behavior can be non-classical. We consider a discrete-time quantum walk on n-cycle subject to a random coin-dependent phase shift at a single position. This finite system, whose evolution is described by only two Kraus operators, can exhibit all kinds of asymptotic behavior observable in quantum Markov chains: it either evolves towards a maximally mixed state, or partially mixed state, or tends to an oscillatory motion on an asymptotic orbit. We find that the asymptotic orbits do not have a product structure, therefore the corresponding states can manifest entanglement between the position and the coin degrees of freedom, even if the system started in a product state.

quant-ph↗

arXiv2019

Pre- and post-selection paradoxes in quantum walks

Many features of single-partite quantum walks can be simulated by classical waves. However, it was recently experimentally shown that some temporal sequences of measurements on a quantum walker do not admit a classical description in terms of macro-realistic theories. Here, we extend this observation and present pre- and post-selection scenarios in quantum walks leading to logical paradoxes. Such paradoxes were recently shown to be equivalent to proofs of contextuality, therefore we provide an additional argument for non-classicality of a quantum walk model. The assumptions behind the claims of non-classicality (including contextuality and violations of macro-realism) are also discussed.

quant-ph↗

arXiv2019

Assembly of 2N entangled fermions into multipartite composite bosons

An even number of fermions can behave in a bosonic way. The simplest scenario involves two fermions which can form a single boson. But four fermions can either behave as two bipartite bosons or further assemble into a single four-partite bosonic molecule. In general, for 2N fermions there are many possible arrangements into composite bosons. The question is: what determines which fermionic arrangement is going to be realized in a given situation and can such arrangement be considered truly bosonic? This work aims to find the answer to the above question. We propose an entanglement-based method to assess bosonic quality of fermionic arrangements and apply it to study how the ground state of the extended one-dimensional Hubbard model changes as the strength of intra-particle interactions increases.

quant-ph↗

arXiv2019

Sculpting out quantum correlations with bosonic subtraction

We present a method to extract M-partie bosonic correlations from an N-partite maximally symmetric state (M < N) with the help of successive applications of single-boson subtractions. We also propose an experimental photonic setup to implement it that can be done with the present technologies.

quant-ph↗

arXiv2019

Disproving hidden variable models with spin magnitude conservation

The squares of the three components of the spin-s operators sum up to $s(s+1)$. However, a similar relation is rarely satisfied by the set of possible spin projections onto mutually orthogonal directions. This has fundamental consequences if one tries to construct a hidden variable (HV) theory describing measurements of spin projections. We propose a test of local HV-models in which spin magnitudes are conserved. These additional constraints imply that the corresponding inequalities are violated within quantum theory by larger classes of correlations than in the case of standard Bell inequalities. We conclude that in any HV-theory pertaining to measurements on a spin one can find situations in which either HV-assignments do not represent a physical reality of a spin vector, but rather provide a deterministic algorithm for prediction of the measurement outcomes, or HV-assignments represent a physical reality, but the spin cannot be considered as a vector of fixed length.

quant-ph↗

arXiv2018

From classical to quantum walk via erasure of which-way information

Decoherence transforms a ballistic quantum walk into a diffusive classical random walk. After each step the environment measures the particle's path and the outside world gets to know the which-way information. The relation between the which-way information and the classicality of the spatial distribution is clearly visible in the multi-coin quantum walk in which the information about particle's path is encoded in the multi-coin degree of freedom. The more information is stored on the coins, the more classical and diffusive the spatial distribution is. Here, we propose a generalized version of the quantum eraser scenario that allows for complex erasure strategies. We show that the which-way information can be erased from the coins and the ballistic features in the spatial probability distribution can be recovered.

quant-ph↗

arXiv2018

On dynamical stability of composite quantum particles: when entanglement is enough and when interaction is needed

We consider an evolution of two elementary quantum particles and ask the question: under what conditions such a system behaves as a single object? It is obvious that if the attraction between the particles is stronger than any other force acting on them the whole system behaves as one. However, recent insight from the quantum information theory suggests that in bipartite systems it is not attraction per se that is responsible for the composite nature, but the entanglement between the parts. Since entanglement can be present between the subsystems that interacted in the past, but do not interact anymore, it is natural to ask when such an entangled pair behaves as a single object. We show that there are situations when entanglement is enough to observe single-particle behaviour. However, due to the no-signalling condition, in general an interaction, or a post-selective measurement, is necessary for a complex collective behaviour.

quant-ph↗

arXiv2018

Monogamy of particle statistics in tripartite systems simulating bosons and fermions

In the quantum world correlations can take form of entanglement which is known to be monogamous. In this work we show that another type of correlations, indistinguishability, is also restricted by some form of monogamy. Namely, if particles A and B simulate bosons, then A and C cannot perfectly imitate fermions. Our main result consists in demonstrating to what extent it is possible.

quant-ph↗

arXiv2018

From contextuality of a single photon to realism of an electromagnetic wave

Violations of Bell inequalities have been an incontestable indicator of non-classicality since the seminal paper by John Bell. However, recent claims of Bell inequalities violations with classical light have cast some doubts on their significance as hallmarks of non-classicality. Here, we challenge those claims. The crux of the problem is that such classical experiments simulate quantum probabilities with intensities of classical fields. However, fields intensities measurements are radically different from single-photon detections, which are primitives of any genuine Bell experiment. We show that this fundamental difference between field intensities measurements and single photon detections shifts the classical bound of relevant Bell inequalities to its algebraic limit, leaving no place for their violations.

quant-ph↗

arXiv2017

Generalized Probabilistic Description of Noninteracting Identical Particles

We investigate an operational description of identical noninteracting particles in multiports. In particular we look for physically motivated restrictions that explain their bunching probabilities. We focus on a symmetric 3-port in which a triple of superquantum particles admitted by our generalized probabilistic framework would bunch with probability 3/4. The bosonic bound of 2/3 can then be restored by imposing the additional requirement of product evolution of certain input states. These states are characterized by the fact that, much like composite systems, their entropy equals the sum of entropies of its one-particle substates. This principle is however not enough to exclude the possibility of superquantum particles in higher-order multiports.

quant-ph↗

arXiv2017

Nonlocal bunching of composite bosons

It was suggested that two entangled fermions can behave like a single boson and that the bosonic quality is proportional to the degree of entanglement between the two particles. The relation between bosonic quality and entanglement is quite natural if one takes into account the fact that entanglement appears in bound states of interacting systems. However, entanglement can still be present in spatially separated subsystems that do not interact anymore. These systems are often a subject of studies on quantum nonlocality and foundations of quantum physics. Here, we ask whether an entangled spatially separated fermionic pair can exhibit bosonic properties. We show that in certain conditions the answer to this question can be positive. In particular, we propose a nonlocal bunching scenario in which two such pairs form an analogue of a two-partite bosonic Fock state.

quant-ph↗

arXiv2016

Contextuality of Identical Particles

A generalisation of quantum contextuality to the case of many indentical particles is presented. The model consists of a finite collection of modes that can be occupied by N particles, either bosons or fermions. Measurement scenarios allow one to measure occupation of each mode in at least two different measurement contexts. The system is said to be non-contextual if the occupation numbers can be assigned to modes in each measurement scenario. The assignment is done under the non-contextuality assumption, i.e., an occupation number assigned to a mode does not depend on a scenario in which this mode is measured. In addition, the total number of particles has to be conserved, therefore the sum of occupation numbers in each measurement context is equal to N. For N=1 the model does not differ from the standard contextuality scenario. However, for N>1 the problem reveals new complex features. In particular, it is shown that a type of contextuality exhibited by the system (state-dependent, state-independent, or non-contextual) depends on the type and the number of particles. Further properties of this model and open problems are also discussed.

quant-ph↗

arXiv2016

Duality in entanglement of macroscopic states of light

We investigate duality in entanglement of a bipartite multi-photon system generated from a coherent state of light. The system can exhibit polarization entanglement if the two parts are distinguished by their parity, or parity entanglement if the parts are distinguished by polarization. It was shown in [PRL 110, 140404 (2013)] that this phenomenon can be exploited as a method to test indistinguishability of two particles and it was conjectured that one can also test indistinguishability of macroscopic systems. We propose a setup to test this conjecture. Contrary to the previous studies using two-particle interference effect as in Hong-Ou- Mandel setup, our setup neither assumes that the tested state is composed of single particles nor requires that the total number of particles be fixed. Consequently the notion of entanglement duality is shown to be compatible with a broader class of physical systems. Moreover, by observing duality in entanglement in the above system one can confirm that macroscopic systems exhibit quantum behaviour. As a practical side, entanglement duality is a useful concept that enables adaptive conversion of entanglement of one degree of freedom (DOF) to that of another DOF according to varying quantum protocols.

quant-ph↗

arXiv2016

How to observe duality in entanglement of two distinguishable particles?

The entanglement between two bosons or fermions can be accessed if there exists an auxiliary degree of freedom which can be used to label and effectively distinguish the two particles. For some types of entanglement between two indistinguishable particles one can observe duality, i.e., if the entanglement is present in the Hilbert space H and an auxiliary Hilbert space H' is used to label the particles, then if we used H as a label the entanglement would be present in H'. For distinguishable particles this effect does not occur because of superselection rules which prevent superpositions of different types of particles. However, it is known that superselection rules can be bypassed if one uses special auxiliary states that are known as reference frames. Here we study properties of reference frames which allow for an observation of a duality in entanglement between two distinguishable particles. Finally, we discuss the consequences of this result from the resource-theoretic point of view.

quant-ph↗

arXiv2016

Three-dimensional visualization of a qutrit

We present a surprisingly simple three-dimensional Bloch sphere representation of a qutrit, i.e., a single three-level quantum system. We start with a symmetric state of a two-qubit system and relate it to the spin-1 representation. Using this representation we associate each qutrit state with a three-dimensional vector $\mathbf{a}$ and a metric tensor $\mathbf{\hatΓ}$ which satisfy $\mathbf{a}\cdot \mathbf{\hatΓ} \cdot \mathbf{a}\leq 1$. This resembles the well known condition for qubit Bloch vectors in which case $\mathbf{\hatΓ}=\hat{I}$. In our case the vector $\mathbf{a}$ corresponds to spin-1 polarisation, whereas the tensor $\mathbf{\hatΓ}$ is a function of polarisation uncertainties. Alternatively, $\mathbf{a}$ is a local Bloch vector of a symmetric two-qubit state and $\mathbf{\hatΓ}$ is a function of the corresponding correlation tensor. We also discuss how a purity of states and state-dynamics is depicted in our representation.

quant-ph↗

arXiv2016

Investigating nonclassicality of many qutrits by symmetric two-qubit operators

We introduce a new method of investigating qutrit nonclassicality by translating qutrit operators to symmetric two-qubit operators. We show that this procedure partially resolves the discrepancy between maximal qutrit entanglement and maximal nonclassicality of qutrit correlations. Namely we express Bell operators corresponding to qutrit Bell inequalities in terms of symmetric two-qubit operators, and analyze the maximal quantum violation of a given Bell inequality from the qubit perspective. As an example we show that the two-qutrit CGLMP(Collins-Gisin-Linden-Massar-Popescu) Bell inequality can be seen as a combination of Mermin's and CHSH (Clauser-Horne-Shimony-Holt) qubit Bell inequalities, and therefore the optimal state violating this combination differs from the one which corresponds to the maximally entangled state of two qutrits. In addition, we discuss the same problem for a three qutrit inequality. We also demonstrate that the maximal quantum violation of the CGLMP inequality follows from complementarity of correlations.

quant-ph↗

arXiv2015

Quantum information approach to Bose-Einstein condensation of composite bosons

We consider composite bosons (cobosons) comprised of two elementary particles, fermions or bosons, in an entangled state. First, we show that the effective number of cobosons implies the level of correlation between the two constituent particles. For the maximum level of correlation, the effective number of cobosons is the same as the total number of cobosons, which can exhibit the original Bose-Einstein condensation (BEC). In this context, we study a model of BEC for indistinguishable cobosons with a controllable parameter, i.e., entanglement between the two constituent particles. We find that bi-fermions behave in a predictable way, i.e., the effective number of the ground state coboson is an increasing function of entanglement between a pair of constituent fermions. Interestingly, bi-bosons exhibit the opposite behaviour - the effective number of the ground state coboson is a decreasing function of entanglement between a pair of constituent bosons.

quant-ph↗